Question

A potential barrier V volts exists across a P-N junction. The thickness of the depletion region is 'd'. An electron with velocity 'v' approaches P-N junction from N-side. The velocity of the electron crossing the junction is:

• A. $\sqrt{v^2+\frac{2Ve}{m}}$
• B. $\sqrt{v^2-\frac{2Ve}{m}}$
• C. v
• D. $\sqrt{\frac{2Ve}{m}}$

Answer 1

The correct option is B $\sqrt{v^2-\frac{2Ve}{m}}$

R.E.F image

AS we know that the electric

field due to the voltage 1 potential

barrier is such that it opposes

the flow of electron from N-region

to P- region. So,

$\frac{mv{f}^2}{2}-\frac{m{v}^2}{2}=\Delta KE$

$\Delta KE=-ve$

So, $\frac{mv{f}^2}{2}-\frac{m{v}^2}{2}=-ve$

$\Rightarrow v_f=\sqrt{v^2-\frac{2ve}{m}}$

Option $-B$ is correct.